Probabilistic Automaton - p-adic Languages

p-adic Languages

The p-adic languages provide an example of a stochastic language that is not regular, and also show that the number of stochastic languages is uncountable. A p-adic language is defined as the set of strings in the letters such that

L_{\eta}(p)=\{0.n_1n_2n_3 \ldots \vert 0\le n_k<p \text{ and }
0.n_1n_2n_3\ldots > \eta \}

That is, a p-adic language is merely the set of real numbers, written in base-p, such that they are greater than . It is straightforward to show that all p-adic languages are stochastic. However, a p-adic language is regular if and only if is rational. In particular, this implies that the number of stochastic languages is uncountable.

Read more about this topic:  Probabilistic Automaton

Famous quotes containing the word languages:

    People in places many of us never heard of, whose names we can’t pronounce or even spell, are speaking up for themselves. They speak in languages we once classified as “exotic” but whose mastery is now essential for our diplomats and businessmen. But what they say is very much the same the world over. They want a decent standard of living. They want human dignity and a voice in their own futures. They want their children to grow up strong and healthy and free.
    Hubert H. Humphrey (1911–1978)